Sampling Unnormalized Probabilities: An Alternative to the Metropolis--Hastings Algorithm

Markov chain Monte Carlo methods are now hugely popular and are used in all aspects of scientific learning. One of the most widely used and efficient methods is the Metropolis--Hastings algorithm. In this note, we introduce an alternative to the Metropolis--Hastings sampler when the state space is countably infinite and the stationary or target distribution is represented by a set of unnormalized probabilities. We illustrate with a comparison of the Metropolis--Hastings sampler.